Excerpts from fons's message of 2010-07-22 22:36:58 +0200: > On Thu, Jul 22, 2010 at 09:31:09PM +0200, lieven moors wrote: > > > Hi Fons, I'm a fool to even try to answer this question. > > But I couldn't resist... > > :-) > > > Let's suppose we have two sounds A and B, > > and sound B has been measured as being twice as loud as A, > > by somebody. In order to be able to say that, that person needs > > some kind of reference measurement unit, the equivalent of a > > measurement stick. That unit has to satisfy two requirements. > > It has to be big enough, so that people can agree some difference > > is being measured, and it has to be small enough, so that a multiples > > of that unit fit into a realistic range. There is a requirement of maximum > > precision (the smallest value we can measure), and a requirement of > > minimum precision. The question is, what kind of measurement stick > > is being used by that person. > > Not really. If A is 'twice' B, either A or B can act as the reference. > > I'm pretty sure that if you'd do the experiment to find out when > people think that an object B is twice as big as another object A > (without introducing optical illusions), you'd find that it's quite > close to a factor of 2. This is because we can easily imagine two > A's side by side, which would be 'twice as big' as one A. > Can we do something similar with 'loudness' ? As I wrote, the > only option I see is to consider two equal sources to be 'twice > as loud' as one of them, but that doesn't work out. > > Given this, what you write does make sense - there must be some > 'stick' rather than a real comparison of A to B. But what is it > based on ? If most people do agree on some value for 'twice as > loud', even with a large variation, there must be some physical > ground for this. But what is it ? And a related question: iff > there is some 'unit' even a variable one depending on frequency > etc., why can't we imagine that unit ? Why don't we 'see' the > stick ? > > > First of all, we can assume that the length of that stick will be depend > > on the range of possible input values that we observe, and that we want > > to measure. If we want to measure the size of a road, we will probably > > use kilometers, instead of meters. In the same way, when our ears want > > to measure the amplitude of a sound, our ears will use smaller or bigger > > units, depending on the ranges observed. What are the ranges we observe? > > Let's assume that humans are perfect, and observe everything that we > > can observe with SPL meters. We could do a statistical investigation > > on a number of people, and make charts of everything they hear. > > In these charts we would see what frequencies they are exposed to, > > and what the minimum and maximum SPL's are for that frequencies. > > After more analyses, we would have one chart that could be > > representative for most people. > > This is basically what has been done more than 50 years ago, with > the known results: the objective ratio corresponding to 'twice as > loud' depends on frequency, absolute level, etc. > > > From that chart we could get an estimate of the size of the measurement > > unit. Frequencies with with bigger SPL variations would be measured > > with bigger units, and visa versa. And from this we could deduce what > > the minimum precision is for a certain frequency, when we say it is twice > > as loud. To satisfy the requirement of maximum precision, we should > > take into account the smallest observable differences for every frequency > > in the spectrum. > > 'Smallest observable difference' has been measured as well. It should > relate in some way to 'twice as loud', but I haven't verified this. > OTOH, knowing the smallest observable difference does not help to > define what 'twice as loud' is supposed to be. > > Another poster mentioned that he found it quite difficult to work > out what 'twice as loud' means for him - and I do believe that is > touching on the real problem: if you start *thinking* about it > rather than just following your 'gut feeling', how sure can you > still be of your impression of 'twice as loud' ? How stable is it > in the face of doubt ? > > Keep on thinking !
We may be comparing the wrong thing when we compare with the size of objects to loudness. It's relatively easy to say that the interval between sound B and C is twice as long as the interval between A and B (given the interval and the length of the sound is in a certain range). This is probably closer to the object size comparison. I wonder how well we can judge something like twice the brightness. -- Regards, Philipp -- "Wir stehen selbst enttäuscht und sehn betroffen / Den Vorhang zu und alle Fragen offen." Bertolt Brecht, Der gute Mensch von Sezuan _______________________________________________ Linux-audio-dev mailing list [email protected] http://lists.linuxaudio.org/listinfo/linux-audio-dev
